Physical parameterization : Cloud microphysics

Axel SeifertDeutscher Wetterdienst

Physical parameterizations (FE14)

The role of cloud microphysics

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Cloud microphysical schemes have to describe the formation, growth andsedimentation of water particles (hydrometeors). They provide the latent heating rates for the dynamics.

Cloud microphysical schemes are a central part of every model of the atmosphere. In numerical weather prediction they are important forquantitative precipitation forecasts.

In climate modeling clouds are crucial due to their radiative impact, and aerosol-cloud-radiation effects are a major uncertainty in climate models.

Clouds in the DWD models

� Grid-scale clouds (microphysics scheme)Parameterization of resolved clouds and precipitation. Cloud variables aretreated by prognostic equations including advection.

� Subgrid convective clouds (convection scheme)Convection is parameterized and diagnosed based on the large-scaleenvironmental conditions. No advection, no history.

� Cloud cover schemeCombines grid-scale, convective, and diagnostic subgrid stratiform clouds tototals values that are passed to the radiation.

� Note that both, COSMO and ICON, do not allow subgrid stratiform clouds toform precipitation. All prognostic clouds have a cloud fraction of 1. This is quitedifferent from other models like, for example, the IFS.

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Saturation adjustment

� We assume that water vapor and liquid water are in thermodynamic equilibrium

� After advection and diffusion the model is not in thermodynamic equilibrium. We have to adjust the thermodynamic state, T, qv and qc, to ensureequilibrium.

� From energy or enthalpy conservation we can derive an equation for the newtemperature T1:

where qsat(T1) is the saturation mixing ratio. This equation is solved by a Newton iteration. Note that ICON uses the cv formulation shown here, whereasCOSMO uses cp.

� This approach has been used in cloud-resolving models since the 1960s. Most global models use a different approach and apply a subgrid diagnostic.

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Cloud microphysical processes

Evaporation and condensation of clouddroplets are parameterized by thesaturation adjustment scheme.

Autoconversion is an artificial process introduced by the separation of cloud droplets and rain. Parameterization of the process is quite difficult and many different schemes are available.

Evaporation of raindrops can be very important in convective systems, since it determines the strength of the cold pool. Parameterization is not easy, since evaporation is very size dependent.

Even for the warm rain processes a lot of things are unknown or in discussion fordecades, like effects of mixing / entrainment on the cloud droplet distribution, effects of turbulence on coalescence, coalescence efficiencies, collisionalbreakup or the details of the nucleation process. In NWP models such detailsare usually neglected.

Cloud microphysical processes

Conversion processes , like snow to graupel conversion by riming, are very difficult to parameterize but very important in convective clouds.

Especially for snow and graupel theparticle properties like particle densityand fall speeds are important parameters.

Aggregation processes assume certaincollision and sticking efficiencies, which arenot well known.

Most NWP models do not include hailprocesses like wet growth, partial meltingor shedding.

The so-called ice multiplication (e.g. Hallet-Mossopprocess) may be very important, but is still not wellunderstood. This includes the fragementation of icecrystals.

Spectral formulation of cloud microphysics

We define the drop size distribution f(x) as the number of drops per unitvolume in the mass range [x,x+dx].For f(x) we can then derive the following budget equation for warm-rain processes

with

The gravitational collision-coalescence kernel

The effects of in-cloud turbulenceon the collision frequency is a current research topic. Recentresults indicate that turbulence cansometimes enhance the rain formation process.

Bulk microphysical schemes

Instead of f(x) only moments of the size distribution are explicitly predicted like theliquid water content:

or the number concentration of particles:

maybe even a third one, like the sixth moment (reflectivity)

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Bin vs. bulk microphysics

x ∈ {m,D}

Another alternative are Monte-Carlo Lagrangianschemes , which are similar to spectral bin models. Currently we are implementing such a scheme in ICON, which will become our new reference.

Increasing complexity of bulk microphysicsmodels over the last decades

Two-moment schemes are becoming more and more the standard in research and are even an option forNWP. A three-moment scheme has been published by Milbrandt and Yau (2005). A recent developmentare prognostic properties schemes for ice microphysics (Morrison & Milbrandt, P3 scheme).

➧ DWD one-moment schemes are similarto Lin et al. (1983) and Rutledge andHobbs (1984).

➧ DWD two-moment scheme has hail(introduced by U. Blahak and H. Noppel in 2008)

Kessler‘s warm -rain scheme

In 1969 Kessler published a very simple warm-rain parameterization which is still used in many bulk schemes.

„As we know, water clouds sometimes persist for a long time without evidence ofprecipitation, but various measurements show that cloud amounts > 1 g/m3 areusually associated with production of precipitation. It seems reasonable to modelnature in a system where the rate of cloud autoconversion increases with the cloudcontent but is zero for amounts below some threshold.“

(E. Kessler: On the Distribution and Continuity of Water Substance in Atmospheric Circulation, Meteor. Monogr. , 1969)

Assuming a Gamma distribution forcloud droplets

the following autoconversion can be derived from the spectral collection equation

with a universal function

A one-moment version of this autoconversion scheme is implemented in the all microphysics schemes of ICON (even in the so-called Kessler scheme).

A two-moment warm -rain scheme

The colored lines represent solutionsof the spectral collection equation forvarious initial conditions.

The dashed line is the fit:

This function describes thebroadening of the cloud dropletsize distribution by collisionsbetween cloud droplets.

Dynamic similarity

no rain no cloud

optimum atLc = 0.9 L

Parameterization of sedimentation:An example how to derive a bulk microphysics equation

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Parameterization of sedimentation:

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Parameterization of sedimentation:

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The COSMO/ICON two -category ice scheme(also known as the ‘cloud ice scheme’)

file: gscp_cloudice.f90 subroutine: cloudicenamelist setting: itype_gscp=3

• Includes cloud water, rain, cloud ice and snow.

• Prognostic treatment of cloud ice, i.e., non-equilibrium growth by deposition.

• Developed for the 7 km grid and coarser.

• Only stratiform clouds, graupelformation is neglected.

The COSMO three-category ice scheme(also known as the ‘graupel scheme’)

file: gscp_graupel.f90subroutine: graupelnamelist setting: itype_gscp=4

• Includes cloud water, rain, cloud ice, snow and graupel.

• Graupel has much higher fall speeds compared to snow

• Developed for the 2.8 km grid, e.g., DWD’s convection-resolving COSMO-DE.

• Necessary for simulation without parameterized convection. In this case the grid-scale microphysics scheme has to describe all precipitating clouds.

Variable snow intercept parameter

� The snow size distribution can now adjust to different conditionsas a function of temperature and snow mixing ratio.

� This will (hopefully) give more accurate estimates of the various microphysical process rates.

higher qs

lower qs

variable interceptf(D)

D

higher T

lower T

variable interceptf(D)

D

higher qs

lower qs

constant intercept f(D)

D

N0,s

Using a parameterization of Field et al. (2005, QJ) based on aircraft measurementsall moments of the snow PSD can be calculated from the mass moment:

Assuming an exponential distribution for snow, N0,s can easily be calculated using the 2nd moment, proportional to qs, and the 3rd moment:

Now we have parameterized N0 as a function of temperature and snow mixing ratio.

Variable snow intercept parameter: An empirical parameterization

Variable snow intercept parameter (continued)

The dominant effect is the temperature dependency, which represents the size effect of aggregation, i.e. on average snow flakes at warmer temperature are larger.

This dependency has already been pointed out be Houze et al. (1979, JAS) and is parameterized in many models using N0,s(T).

The two -moment microphysics schemeofthe COSMO model

Currently not part of the official code, but can be added easily. Should become official with COSMO 5.6

• Prognostic number concentration for all particle classes, i.e. explicit size information.

• Prognostic hail.

• Aerosol-cloud-precipitation effects can be simulated

• Using 12 prognostic variables the scheme is computationally expensive and not well suited for operational use.

Case study 20 Juli 2007: Cold Front / Squall Line

� More intense squall line with two-moment scheme � Aerosol effect can slightly modify the intensity and spatial distribution.

accumulated precip in mm

Radar (RY) ONE-MOMENT SB-CLEAN SB-POLLUTED

AVG: 3.4 mm AVG: 2.8 mm AVG: 3.4 mm AVG: 3.5 mm

Case study 11 Nov 2007

� Only weak sensitivity to cloud microphysics. No significant difference between one- and two-moment scheme.

� Orographic precipitation enhancement is weaker for ‘polluted’ aerosol assumptions.

Gauges (REGNIE) ONE-MOMENT SB-CLEAN SB-POLLUTED

AVG: 11.7 mm AVG: 10.7 mm AVG: 11.4 mm AVG: 11.0 mm

accumulated precip in mm

Some precipitation statistics

COSMO-DE has an pretty goodprecip statistics, with a slightunderestimation for low tomoderate rainfall and an overestimation of strong rain.

The forecast skill for precipitationis of course far from perfect, but this is very much related topredictability issues.

Precipitation distribution for 24 h accumulatedprecipitation from observations (solid line) andCOSMO-DE (dashed line) for summer 2011.

Some precipitation statistics

A more common metric is thefrequency bias (FBI), whichcompares the frequency ofoccurence with measurements(FBI of 1 is perfect).

For most years COSMO-DE shows an underestimation of lowintensities and an overestimationof the highest intensities. This iswhat we expect from an underresolved convection-permitting model.

Frequency bias as a function of precipitationamount for different years of COSMO-DE.

Some precipitation statistics

This ETS is an actual score andrequires point-based location(ETS of 1 is perfect).

Point wise precip scores decreaserapidly with intensity and sufferfrom double counting.

COSMO showed a niceimprovement in 2013, but this was only partly due to modelimprovements. Some part was just year to year variability.

Equitable threat score (ETS) as a function ofprecipitation amount for different years ofCOSMO-DE.

Some precipitation statistics

The fraction skill score is a popular „fuzzy“ score toleratessome mismatch in location(FSS of 1 is perfect).

Again we see the decreasetowards higher precip amountsand a considerable year to yearvariability.

Fraction skill score (FSS) as a function ofprecipitation amount for different years ofCOSMO-DE.

A forecast example of the pre-operational COSMO -D2

The End

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ICON namelist parameters:

inwp_gscp: main switch for microphysics schemesinwp_gscp=1: operational cloud ice schemeinwp_gscp=2: graupel schemeinwp_gscp=3: two-moment cloud ice (does not work)inwp_gscp=4: two-moment schemeinwp_gscp=5: two-moment scheme with progn.

CCN and IN (only idealized cases).

qi0: Threshold for cloud ice autoconversion (default zero)qc0: Threshold for cloud water autoconversion (zero, not used!)

mu_rain: Shape parameter of gamma distribution of rain mu_snow: Shape parameter of gamma distribution of snow

icpl_aero_gscp: switch for coupling of microphysics with aerosol climatology(activation and autoconversion of cloud droplets), only forinwp_gscp=1. Default 0, but 1 operationally.

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Some internal switches in gscp=1:

lstickeff = .true./.false. modification of sticking efficiency (ice-ice, ice-snow)

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Reduced sticking efficiencyleads to an increase in QI. This is necessary for the radiationbudget in the tropics.

Switch is .false. by default, but this modification is also part oflorig_icon, which is .true.

The constant minimum valuecan be chosen by the namelistparameter tune_zceff_min(in nwp_tuning_nml)

Some internal switches in gscp=1:

lsedi_ice = .true./.false. switch for sedimentation of cloud ice

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Switch is .false. by default, but this modification is also part oflorig_icon, which is .true.

The pre-factor of the power lawcan be modified with tune_zvz0i in nwp_tuning_nml.

An important parameter is thepre-factor of the snow fallspeed, tune_v0snow, also in nwp_tuning_nml.

Configuration of the two-moment scheme:

Currently there are no namelist parameters for the two-moment scheme. This might change in the future.

In mo_2mom_mcrph_driver.f90

INTEGER, PARAMETER :: cloud_type_default_gscp4 = 2103, ccn_type_gscp4 = 1

ccn_type_gscp4: 1: Hande et al. 2016 CCN activation scheme for 17 April 20146: Segal&Khain 2006 CCN activation scheme, maritime7: Segal&Khain 2006 CCN activation scheme, intermediate8: Segal&Khain 2006 CCN activation scheme, continental9: Segal&Khain 2006 CCN activation scheme, polluted continental

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Configuration of the two-moment scheme:

Currently there are no namelist parameters for the two-moment scheme. This might change in the future.

In mo_2mom_mcrph_driver.f90

INTEGER, PARAMETER :: cloud_type_default_gscp4 = 2103, ccn_type_gscp4 = 1

ice nucleation (2nd digit of cloud_type_default_gscp4):

1: Hande et al. 2015 IN scheme, for average Spring conditions2: Hande et al. 2015 IN scheme, for average Summer conditions3: Hande et al. 2015 IN scheme, for average Autumn conditions4: Hande et al. 2015 IN scheme, for average Winter conditions

6: Phillips et al. IN scheme, high soot, low organics7: Phillips et al. IN scheme, high soot, some organics8: Phillips et al. IN scheme, only mineral dust

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